Which of the following numbers is a factor of 91? ${5,6,10,11,13}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $91$ by each of our answer choices. $91 \div 5 = 18\text{ R }1$ $91 \div 6 = 15\text{ R }1$ $91 \div 10 = 9\text{ R }1$ $91 \div 11 = 8\text{ R }3$ $91 \div 13 = 7$ The only answer choice that divides into $91$ with no remainder is $13$ $ 7$ $13$ $91$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $13$ are contained within the prime factors of $91$ $91 = 7\times13 13 = 13$ Therefore the only factor of $91$ out of our choices is $13$. We can say that $91$ is divisible by $13$.